If you look at various data, I'm showing max to be around 69 to 73 grains. It depends on the brass, seating depth, and a few other factors. If you blow primers at 71, that's a hot load. So about 70 grains is a max load, and you blew primers at 71, so you are past max for your combination of ammo.

Also, do NOT go but a few grains less than max. 7828 and a 257 Wby Mag are combo's that do not work well together as a reduced load or as a minimum load.

Are you just starting at the load that lists the FPS you want in the manual? That breaks like every rule of reloading.

What the book shows as max should be a guide to use as you work up to max in your rifle. You rifle has found max before the book shows with the set up you are running. Also, in the Hornady manual with a Hornady brass and Hornady 100 grain SP, I'm showing 66.8 grains as max with 7828.

For S&G, I ran your info in QuickLoad- 70.0 grains of IMR 7828 with a 100 grain SMK seated to 3.170" is showing to be 62500 psi. So, it's a max or near max load. If you seat the bullet deeper, this will increase the pressure. If the Hornady brass has less case capacity and/or tighter necks than the Wby brass used in the manuals, than this will all raise your pressures. If you knew the speeds with a chronograph, then I could tell you more of where you are on max or not. But with your combination, you have pressure signs at 70, so this should be over max in your rifle with the components you are using. If the others were fine and this one blew and you don't know why, then that's something to figure out.

Winchester large rifle primers?

large rifle magnum.

I rebarrelled a rifle and the load that shot fine in the first barrel was way too hot in the second barrel. Turned out that the second barrel had a real tight chamber. Could be your chamber.

And did you say this rifle was a Weatherby (with freebore) or possibly a non Wby without freebore?

The reason I asked is there are some bad Winchester LR primers in circulation.